Title: Hodge--Tate prismatic crystals of cohomological l.c.i. algebras

Abstract: Hodge--Tate prismatic crystals, which are considered as `imperfect'  $v$-vector bundles, play an important role in the modern theory of $p$-adic non-abelian theory.  In this talk, I will introduce a new classification theorem of Hodge--Tate prismatic crystals on cohomological l.c.i. algebras, which generalizes various classification theorems in the past. In addition, I will introduce some (potential) applications, including a comparison theorem between Hodge--Tate prismatic crystals and generalized representations of geometric valuation rings and a Hodge--Tate type comparison theorem for certain non-smooth formal schemes.

This is a joint work with Xiaoyu Qu.